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49
Block # 4
Block # 1 Block # 2 Block # 3
Figure 6.4. Grid system for the numerical simulation.
Figures 6.12 and 6.13 show the shear stress distribution for By regression, the equation proposed for the correction
S/ B = 1.88 and S/ B = 6. factor ksp giving the influence of the pier spacing on the max-
imum shear stress is
6.8 PIER SPACING EFFECT ON MAXIMUM
max
S
SHEAR STRESS -1.1
ksp = = 1 + 5e B . (6.3)
max (single)
The maximum shear stress max is the maximum shear
stress that exists on the riverbed just before the scour hole
starts to develop. One way to present the data is to plot 6.9 PIER SHAPE EFFECT:
max/max(single) as a function of S/ B (Figure 6.10). The param- NUMERICAL SIMULATION RESULTS
eter max(single) is the value of max for the case of a single pier
in deep water and is given by Equation 6.1. The pier spac- The objective of this parametric study was to obtain the
ing correction factor, ksp, is the ratio max/max(single). The data relationship between the maximum bed shear stress max and
points on Figure 6.14 correspond to the results of the four the shape of rectangular piers (Figure 6.15). One of the
numerical simulations. flume experiments was chosen to perform the numerical
0 .6
0 .5
0 .4
Depth (m)
FANS
E x p e r im e n t y /D = 2
0 .3 E x p e r im e n t y /D = 1
E x p e r im e n t y /D = 0 .5
0 .2
0 .1
0
0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5
V e lo c it y ( m /s )
Figure 6.5. Velocity profile comparison between experiment and numerical simulation at the inlet.

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50
Z = 0.25
X
0.35
Y 0.45
0.65 0.25
0.75
0.55 1.05
0.85
Flow
-1 -0.5 0 0.5 1
X/B
Figure 6.8. Initial bed shear stress distribution (N/m2)
around the pier (H/B = 2, V = 0.3m/s).
simulation. A rectangular pier with a width of 0.061 m was
(a). H/B=0.2 placed vertically in the 1.5-m-wide flume. The velocity was
constant and equal to 0.33 m/s and the water depth was
0.375 m. Four different pier aspect ratios were simulated:
Z
L/ B = 1, 4, 8, and 12. The value of the Reynolds Number
based on the width of the rectangular pier was Re = 20130
X
and the Froude Number based on the width of the rectan-
Y
gular pier was Fr = 0.4267.
Examples of velocity fields are presented in Figures 6.16
and 6.17 for rectangular piers with aspect ratios equal to 0.25
and 4. Figures 6.18 to 6.20 show the maximum bed shear
stress contours around rectangular piers with different aspect
ratios: L/ B = 0.25, 1, and 4. The location of the maximum bed
shear stress was at the front corner of the rectangle. It was
found that the maximum bed shear stress, max, was nearly
constant for any aspect ratio above one. The value of max
2
1.5
Flow
(b). H/B=2 1
Figure 6.6. Velocity vector around pier for (a) H/B = 0.5 -0.43
-0.37
0.2 and (b) H/B = 2. 0.09
Y/D
0.16 0.36 Pier
0 -0.37 -0.30
0.23
0.25
0.56 0.78 1.03 -0.5
-0.43
4.97
2.21 7.33 -1
Flow -1.5
-2
-1 -0.5 0 0.5 1 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2
X/B X/D
Figure 6.7. Initial bed shear stress distribution (N/m2) Figure 6.9. Normalized pressure (p/u2) contours for
around the pier (H/B = 0.2, V = 0.3m/s). H/B = 2 on the riverbed.